The radioactive decay of 238U and 232Th has recently been used to determine ages for some of the oldest stars in the Universe. This has highlighted the need for accurate observational constraints on production models for the heaviest r-process elements which might serve as stable references, notably osmium and iridium. In order to provide a firmer basis for the observed abundances, we have performed laser-induced fluorescence measurements and Fourier Transform Spectroscopy to determine new radiative lifetimes and branching fractions for selected levels in Os I and Ir I. From these data, we determine new absolute oscillator strengths and improved wavelengths for 18 Os I and 4 Ir I lines. A reanalysis of VLT spectra of CS 31082-001 and new results for other stars with Os and Ir detections show that (i): the lines in the UV and λ 4260 Å yield reliable Os abundances, while those at   4135, 4420 Å are heavily affected by blending; (ii): the Os and Ir abundances are identical in all the stars; (iii): the heavy-element abundances in very metal-poor stars conform closely to the scaled solar r-process pattern throughout the range 56 ≤ Z ≤ 77; and (iv): neither Os or Ir nor any lighter species are suitable as reference elements for the radioactive decay of Th and U.